Multiplying Fractions.notebook
Multiplying Fractions.notebook
February 26, 2016
Learning Goal We can relate our knowledge of multiplication of whole numbers to conceptualize what it really means to multiply fractions Success Criteria I can represent the multiplication of fractions using models to clearly demonstrate my thinking and understanding
Multiplying Fractions.notebook
February 26, 2016
The 15 second way.....:) When you multiply fractions: multiply your numerators to get the numerator for your answer (product) multiply your denominators to get the denominator for your answer (product)
example:
(simplified)
Seems pretty simple, right?;). Well, we also need to learn why this works. Not quite as easy to do that.
Multiplying Fractions.notebook
February 26, 2016
Getting Started True statements about multiplying whole numbers: With your elbow partner, justify why each statement is true 1. Multiplication is the same as repeated addition when you add the same number again and again. 2. Times means “groups of.” 3. A multiplication problem can be shown as a rectangle. 4. You can reverse the order of the factors and the product stays the same. 5. You can break numbers apart to make multiplying easier. 6. When you multiply two numbers, the product is larger than the factors unless one of the factors is zero or one. *Are all these rules still applicable when we are multiplying with fractions?
Multiplying Fractions.notebook
February 26, 2016
Working On It
1. Multiplication is the same as repeated addition when you add the same number again and again.
Do you think this is true about multiplying fractions? Justify. 6 x 1/2
Multiplying Fractions.notebook
February 26, 2016
2. Times means “groups of.” “Does it make sense to read ‘six times one-half‛ as ‘six groups of one-half‛? one-half of six?”
Multiplying Fractions.notebook
February 26, 2016
Does this apply to fractions? 3. A multiplication problem can be shown as a rectangle.
How can you make a model for fractions?
Multiplying Fractions.notebook
February 26, 2016
What if both numbers are fractions? Can I model this using a model?
How much of the one by one square isn't shaded?
Multiplying Fractions.notebook
February 26, 2016
True?
4. You can reverse the order of the factors and the product stays the same.
If we think about the times sign as ‘groups of,‛ then one-half times six should be ‘one-half groups of six.‛ But that doesn‛t sound right. It does make sense, however, to say ‘one- half of a group of six,‛ or ‘one-half of six,‛ and leave off the ‘groups‛ part. Both sound better, and they‛re still the same idea. What do you think ‘one-half of six‛ could mean?”
Multiplying Fractions.notebook
February 26, 2016
True?
5. You can break numbers apart to make multiplying easier.
Talk with your neighbour about how you could apply this statement to the problem six times one-half.
Multiplying Fractions.notebook
February 26, 2016
For example:
or
Multiplying Fractions.notebook
February 26, 2016
True?
6. When you multiply two numbers, the product is larger than the factors unless one of the factors is zero or one. Justify whether you think this is true or not with an example.
Revised: When you multiply two numbers, the product is larger than the factors unless one of the factors is zero or one OR smaller than one.
Multiplying Fractions.notebook
February 26, 2016
Connect & Reflect
How to conceptualize what multiplying fractions actually means instead of understanding a "rule"
Multiplying Fractions.notebook
February 26, 2016
How can we use cuisenaire rods to model multiplication of fractions? Let's try with 3/4 x 2/5
Multiplying Fractions.notebook
February 26, 2016
How can we use cuisenaire rods to model multiplication of fractions? Let's try with 3/4 x 2/5
1. Take your two denominators (4 purple and 5 yellow) and stack one vertically and one horizontally until you can make a overlapped rectangle (they won't overlap perfectly because of the space between the rods)
Multiplying Fractions.notebook
February 26, 2016
How can we use cuisenaire rods to model multiplication of fractions? Let's try with 3/4 x 2/5
2. make an equivalent fraction for with a denominator of 20 (LCD) for each of the fractions
(they won't overlap perfectly because of the space between the rods)
Multiplying Fractions.notebook
February 26, 2016
How can we use cuisenaire rods to model multiplication of fractions? Let's try with 3/4 x 2/5
3. overlap your numerators on your rectangle grid.
(they won't overlap perfectly because of the space between the rods)
Multiplying Fractions.notebook
February 26, 2016
How can we use cuisenaire rods to model multiplication of fractions? Let's try with 3/4 x 2/5
4. count how many squares the green and red share this is your numerator. Count how many squares are in your rectangle this is your denominator (they won't overlap perfectly because of the space between the rods)
Multiplying Fractions.notebook
February 26, 2016
How can we use cuisenaire rods to model multiplication of fractions? Let's try with 3/4 x 2/5
Multiplying Fractions.notebook
February 26, 2016
Homework : Demonstrate your ability to multiply fractions using a model. 1. 1/4 x 3/6 2. 4/5 x 1/3 3. 2/3 x 4/6
4. Three-quarters of a cake was left over from the Mad Hatter‛s Tea Party. Alice ate 2/3 of the leftover cake. How much of the whole cake did she eat? Create a pictorial model that could be used to solve the problem.
Multiplying Fractions.notebook
February 26, 2016
IEP Homework 1. Turn 4 x 3/10 into a repeated addition statement. Solve and simplify your answer. a) 6/5
b) 3/40
c) 7/10
d) 43/10
2. Draw a model that represents 3 x 4/7 as a repeated addition question. Solve and simplify.
3. Rewrite this question as a multiplication question. Find the product (bonus). 2/5 + 2/5 + 2/5 + 2/5 + 2/5 + 2/5 + 2/5 4. It takes Jim 2 3/4 h to make a model car and 1 1/4 h to make a model plane. How long will it take him to make 2 of each?
Multiplying Fractions.notebook
February 26, 2016
Extra Practice Questions We Made (you can make your own practice easily:) (make proper x proper) 3/4 x 2/5
6/11 x 22/43
(make proper x improper) 4/7 x 8/7
2/19 x 56/4
(make mixed x proper)
3 1/5 x 7/10
4 2/11 x 18/21
(make mixed x improper) 5 2/12 x 81/7
3 1/7 x 61/4 x 3/12 (you can have more than two numbers)
Multiplying Fractions.notebook
Make your own word problems to make your own word problems, you need: Two people a place and a thing
February 26, 2016
Multiplying Fractions.notebook
February 26, 2016
Make your own word problems Our attempt to make your own word problems, you need: Two people (Jayden and Charlotte) a place (Jail) and a thing (Popeye's Chicken)
In jail, Jayden and Charlotte earned a Popeye's Chicken dinner as a reward for good behaviour. Charlotte gets the chicken first and she eats 7/10 of the chicken. Jayden eats 3/4 of the leftover chicken. a) How much chicken did Jayden eat? b) There were 80 total pieces of chicken ordered. How many pieces were left over after both people ate?
Multiplying Fractions.notebook
February 26, 2016
In jail, Jayden and Charlotte earned a Popeye's Chicken dinner as a reward for good behaviour. Charlotte gets the chicken first and she eats 7/10 of the chicken. Jayden eats 3/4 of the leftover chicken. a) How much chicken did Jayden eat? b) There were 80 total pieces of chicken ordered. How many pieces were left over after both people ate?
Here's what most of you did 7/10 x 3/4 = 21/40 Jayden ate 21/40 of the chicken.
What did you miss?
Multiplying Fractions.notebook
February 26, 2016
In jail, Jayden and Charlotte earned a Popeye's Chicken dinner as a reward for good behaviour. Charlotte gets the chicken first and she eats 7/10 of the chicken. Jayden eats 3/4 of the leftover chicken. a) How much chicken did Jayden eat? b) There were 80 total pieces of chicken ordered. How many pieces were left over after both people ate?
17/10 = 3/10 of the chicken is left after Charlotte is done 3/4 of 3 /10 = 3/4 x 3/10 = 9/40 Jayden ate 9/40 of the chicken 7/10 (Charlotte) = 28/40 + 9/40 (Jayden) = 37/40 were eaten altogether 37/40 (x 2) = 74/80 were eaten, so 6 of 80 pieces were left over
Multiplying Fractions.notebook
Visual Model
February 26, 2016
February 26, 2016
Learning Goal We can relate our knowledge of multiplication of whole numbers to conceptualize what it really means to multiply fractions Success Criteria I can represent the multiplication of fractions using models to clearly demonstrate my thinking and understanding
Multiplying Fractions.notebook
February 26, 2016
The 15 second way.....:) When you multiply fractions: multiply your numerators to get the numerator for your answer (product) multiply your denominators to get the denominator for your answer (product)
example:
(simplified)
Seems pretty simple, right?;). Well, we also need to learn why this works. Not quite as easy to do that.
Multiplying Fractions.notebook
February 26, 2016
Getting Started True statements about multiplying whole numbers: With your elbow partner, justify why each statement is true 1. Multiplication is the same as repeated addition when you add the same number again and again. 2. Times means “groups of.” 3. A multiplication problem can be shown as a rectangle. 4. You can reverse the order of the factors and the product stays the same. 5. You can break numbers apart to make multiplying easier. 6. When you multiply two numbers, the product is larger than the factors unless one of the factors is zero or one. *Are all these rules still applicable when we are multiplying with fractions?
Multiplying Fractions.notebook
February 26, 2016
Working On It
1. Multiplication is the same as repeated addition when you add the same number again and again.
Do you think this is true about multiplying fractions? Justify. 6 x 1/2
Multiplying Fractions.notebook
February 26, 2016
2. Times means “groups of.” “Does it make sense to read ‘six times one-half‛ as ‘six groups of one-half‛? one-half of six?”
Multiplying Fractions.notebook
February 26, 2016
Does this apply to fractions? 3. A multiplication problem can be shown as a rectangle.
How can you make a model for fractions?
Multiplying Fractions.notebook
February 26, 2016
What if both numbers are fractions? Can I model this using a model?
How much of the one by one square isn't shaded?
Multiplying Fractions.notebook
February 26, 2016
True?
4. You can reverse the order of the factors and the product stays the same.
If we think about the times sign as ‘groups of,‛ then one-half times six should be ‘one-half groups of six.‛ But that doesn‛t sound right. It does make sense, however, to say ‘one- half of a group of six,‛ or ‘one-half of six,‛ and leave off the ‘groups‛ part. Both sound better, and they‛re still the same idea. What do you think ‘one-half of six‛ could mean?”
Multiplying Fractions.notebook
February 26, 2016
True?
5. You can break numbers apart to make multiplying easier.
Talk with your neighbour about how you could apply this statement to the problem six times one-half.
Multiplying Fractions.notebook
February 26, 2016
For example:
or
Multiplying Fractions.notebook
February 26, 2016
True?
6. When you multiply two numbers, the product is larger than the factors unless one of the factors is zero or one. Justify whether you think this is true or not with an example.
Revised: When you multiply two numbers, the product is larger than the factors unless one of the factors is zero or one OR smaller than one.
Multiplying Fractions.notebook
February 26, 2016
Connect & Reflect
How to conceptualize what multiplying fractions actually means instead of understanding a "rule"
Multiplying Fractions.notebook
February 26, 2016
How can we use cuisenaire rods to model multiplication of fractions? Let's try with 3/4 x 2/5
Multiplying Fractions.notebook
February 26, 2016
How can we use cuisenaire rods to model multiplication of fractions? Let's try with 3/4 x 2/5
1. Take your two denominators (4 purple and 5 yellow) and stack one vertically and one horizontally until you can make a overlapped rectangle (they won't overlap perfectly because of the space between the rods)
Multiplying Fractions.notebook
February 26, 2016
How can we use cuisenaire rods to model multiplication of fractions? Let's try with 3/4 x 2/5
2. make an equivalent fraction for with a denominator of 20 (LCD) for each of the fractions
(they won't overlap perfectly because of the space between the rods)
Multiplying Fractions.notebook
February 26, 2016
How can we use cuisenaire rods to model multiplication of fractions? Let's try with 3/4 x 2/5
3. overlap your numerators on your rectangle grid.
(they won't overlap perfectly because of the space between the rods)
Multiplying Fractions.notebook
February 26, 2016
How can we use cuisenaire rods to model multiplication of fractions? Let's try with 3/4 x 2/5
4. count how many squares the green and red share this is your numerator. Count how many squares are in your rectangle this is your denominator (they won't overlap perfectly because of the space between the rods)
Multiplying Fractions.notebook
February 26, 2016
How can we use cuisenaire rods to model multiplication of fractions? Let's try with 3/4 x 2/5
Multiplying Fractions.notebook
February 26, 2016
Homework : Demonstrate your ability to multiply fractions using a model. 1. 1/4 x 3/6 2. 4/5 x 1/3 3. 2/3 x 4/6
4. Three-quarters of a cake was left over from the Mad Hatter‛s Tea Party. Alice ate 2/3 of the leftover cake. How much of the whole cake did she eat? Create a pictorial model that could be used to solve the problem.
Multiplying Fractions.notebook
February 26, 2016
IEP Homework 1. Turn 4 x 3/10 into a repeated addition statement. Solve and simplify your answer. a) 6/5
b) 3/40
c) 7/10
d) 43/10
2. Draw a model that represents 3 x 4/7 as a repeated addition question. Solve and simplify.
3. Rewrite this question as a multiplication question. Find the product (bonus). 2/5 + 2/5 + 2/5 + 2/5 + 2/5 + 2/5 + 2/5 4. It takes Jim 2 3/4 h to make a model car and 1 1/4 h to make a model plane. How long will it take him to make 2 of each?
Multiplying Fractions.notebook
February 26, 2016
Extra Practice Questions We Made (you can make your own practice easily:) (make proper x proper) 3/4 x 2/5
6/11 x 22/43
(make proper x improper) 4/7 x 8/7
2/19 x 56/4
(make mixed x proper)
3 1/5 x 7/10
4 2/11 x 18/21
(make mixed x improper) 5 2/12 x 81/7
3 1/7 x 61/4 x 3/12 (you can have more than two numbers)
Multiplying Fractions.notebook
Make your own word problems to make your own word problems, you need: Two people a place and a thing
February 26, 2016
Multiplying Fractions.notebook
February 26, 2016
Make your own word problems Our attempt to make your own word problems, you need: Two people (Jayden and Charlotte) a place (Jail) and a thing (Popeye's Chicken)
In jail, Jayden and Charlotte earned a Popeye's Chicken dinner as a reward for good behaviour. Charlotte gets the chicken first and she eats 7/10 of the chicken. Jayden eats 3/4 of the leftover chicken. a) How much chicken did Jayden eat? b) There were 80 total pieces of chicken ordered. How many pieces were left over after both people ate?
Multiplying Fractions.notebook
February 26, 2016
In jail, Jayden and Charlotte earned a Popeye's Chicken dinner as a reward for good behaviour. Charlotte gets the chicken first and she eats 7/10 of the chicken. Jayden eats 3/4 of the leftover chicken. a) How much chicken did Jayden eat? b) There were 80 total pieces of chicken ordered. How many pieces were left over after both people ate?
Here's what most of you did 7/10 x 3/4 = 21/40 Jayden ate 21/40 of the chicken.
What did you miss?
Multiplying Fractions.notebook
February 26, 2016
In jail, Jayden and Charlotte earned a Popeye's Chicken dinner as a reward for good behaviour. Charlotte gets the chicken first and she eats 7/10 of the chicken. Jayden eats 3/4 of the leftover chicken. a) How much chicken did Jayden eat? b) There were 80 total pieces of chicken ordered. How many pieces were left over after both people ate?
17/10 = 3/10 of the chicken is left after Charlotte is done 3/4 of 3 /10 = 3/4 x 3/10 = 9/40 Jayden ate 9/40 of the chicken 7/10 (Charlotte) = 28/40 + 9/40 (Jayden) = 37/40 were eaten altogether 37/40 (x 2) = 74/80 were eaten, so 6 of 80 pieces were left over
Multiplying Fractions.notebook
Visual Model
February 26, 2016
